自由Clifford幺半群和含恒等元的自由半格的图表示

证明了非空集合$X$上自由Clifford幺半群$C_{X}$与双根字树集合$B_{X}$的某个子集并上一个恒等元所得的半群$\\overline{B_{X}}$同构, 并且考察了$B_{X}$与$\\overline{B_{X}}$的关系. 另外, 还证明了含恒等元的自由半格$Y_{X}$与有根字树集合$T_{X}$的某个子集并上一个恒等元所得的半群$\\overline{T_{X}}$同构.     

Clifford分析中二正则函数的性质及某些Riemann边值问题

定义了Clifford分析中一类二正则函数,讨论了它的表示、柯西型积分、Plemelj公式及其他性质,同时研究了二正函数的某些Riemann边值问题,得到了该问题解的具体表示式．     

On the notion of free will in the Free Will Theorem

The (Strong) Free Will Theorem (fwt) of Conway and Kochen (2009) on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will (allowing physicists to “freely choose” the settings of their experiments). This makes the theorem philosophically vulnerable, especially if it is construed as a proof of indeterminism or even of libertarian free will (as Conway & Kochen suggest).However, Cator and Landsman (Foundations of Physics 44, 781–791, 2014) previously gave a reformulation of the fwt that does not presuppose indeterminism, but rather assumes a mathematically specific form of such “free choices” even in a deterministic world (based on a non-probabilistic independence assumption). In the present paper, which is a philosophical sequel to the one just mentioned, I argue that the concept of free will used in the latter version of the fwt is essentially the one proposed by Lewis (1981), also known as ‘local miracle compatibilism’ (of which I give a mathematical interpretation that might be of some independent interest also beyond its application to the fwt). As such, the (reformulated) fwt in my view challenges compatibilist free will à la Lewis (albeit in a contrived way via bipartite epr-type experiments), falling short of supporting libertarian free will.     

柯西中值定理的新证明

利用有限覆盖定理给出了柯西中值定理的新的证明方法,并进一步加深了对柯西中值定理的理解.